# Calculating momentum before and after a collision

1. Jul 18, 2011

### sdoyle1

1. The problem statement, all variables and given/known data
A 1200 kg car traveling north at 14 m/s is rear-ended by a 2000 kg truck traveling at 25 m/s.
a) What is the total momentum before and after the collision?
b)If the car and truck lock bumpers and stick together, what is their speed immediately after the collision?
c) If the care and truck do not lock bumpers and the velocity of the car after the collision is 5 m/s, what is the speed of the truck after the collision?

2. Relevant equations

3. The attempt at a solution
I'm stuck on the concepts and my teachers hasn't gone into detail in class yet. If someone can explain the concepts then I can probably figure out the math.

2. Jul 18, 2011

### thepatient

Momentum is a vector quantity. In this case, you only have one component to worry about.

Formula for momentum P = mv

Also, momentum is conserved in collisions so the net initial momentum of the system is equal to the net final momentum.

3. Jul 18, 2011

### sdoyle1

so would part a) just be a sum of both momentums? Or would I add the masses to get a total mass and multiply it by the total velocity (for both the truck and the car)?

4. Jul 18, 2011

### cupid.callin

Momentum of a particle is defined as the product of the mass and velocity of an object.

The law you will have to use here is the "Law of Conservation of Momentum."
It says that for a system, if net external force acting on it is 0, total momentum will remain constant.

Newton's second law (in original form) is: $F = - \frac{dp}{dt}$

If p is constant, F=0.

5. Jul 18, 2011

### cupid.callin

yes it will be sum of momenta of both truck and car

6. Jul 18, 2011

### sdoyle1

Ok, I have figured out part a. How would it change if the bumpers stick together? Would the mass be the 3200 kg? How about the velocity? Would it just be the total momentum divided by the total weight?

7. Jul 18, 2011

### cupid.callin

this is how collision will work:

truck is moving at higher speed than car. they collide, speed of truck dec. and that of car inc. and at some moment their speeed become equal.
then after that, car's speed inc. and that of truck dec and car starts moving faster than truck

so if they are locked together they will now have same speed and mass as sum of both car and truck